Numeric Simulation of a Glider Winch Launch - RWTH-Aachen

Chair of Flight Dynamics Prof. Dr.-Ing. W. Alles

Study Thesis Numeric Simulation of a Glider Winch Launch

cand. ing. Christoph G. Santel 2008

Advising Tutor: Dipl.-Ing. Jan Nowack communicated by Prof. Dr.-Ing. D. Moormann

Chair of Flight Dynamics RWTH Aachen University

Task The question of the optimized winch launch arises from the current advancements in glider performance and increase in glider mass. As a rst step in modeling the winch launch, a winch, cable and pilot model was introduced into an existing sixdegree-of-freedom glider simulation in MATLAB/Simulink already developed at the Chair of Flight Dynamics. This model is to be enhanced. More comprehensive winch and pilot models shall be congured on the basis of enhanced data that is now available. When possible, the cable should be modeled in FEM. Subsequently, the parameters of the simulation are to be varied in order to gain insight into the optimized winch launch. The following steps are to be completed in the frame of this thesis:

Research of existing research papers and data on the topic

Enhancement of the simulation (winch, cable, pilot behavior)

Variation of simulation parameters (cable properties, weak links, pilot behavior, wind)

Analysis of the results as they pertain to an optimal winch launch

Comprehensive documentation of all work done

iii

Contents

0.1

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 Background

1 2

1.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.2

The Winch Launch . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.3

Necessary Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.4

Development Considerations . . . . . . . . . . . . . . . . . . . . . . .

5

1.5

Simulation Environment in MATLAB/Simulink

6

. . . . . . . . . . . .

2 Models and Simulation 2.1

7

Implemented MATLAB/Simulink Blocks . . . . . . . . . . . . . . . .

8

2.1.1

Aircraft Model

2.1.2

Winch Model

. . . . . . . . . . . . . . . . . . . . . . . . . .

8

. . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.1.3

Cable Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.1.4

Human Controller Models

. . . . . . . . . . . . . . . . . . . .

17

2.1.5

Atmospheric Model / Wind Inuence . . . . . . . . . . . . . .

21

2.2

Provision of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22

2.3

Engagement of Numeric Solution

. . . . . . . . . . . . . . . . . . . .

22

2.4

Further Limits of Models . . . . . . . . . . . . . . . . . . . . . . . . .

23

3 Results 3.1

3.2

24

Reference Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3.1.1

Reference Simulation Settings

. . . . . . . . . . . . . . . . . .

24

3.1.2

Reference Results . . . . . . . . . . . . . . . . . . . . . . . . .

26

. . . . . . . . . . . . . . . . . . . . . . . . .

28

3.2.1

Variation of Parameters

Inuence of Synthetic vs. Steel Cable . . . . . . . . . . . . . .

29

3.2.2

Inuence of Tow Distance

29

3.2.3

Wind Inuence

. . . . . . . . . . . . . . . . . . . . . . . . . .

31

3.2.4

Inuence of Tow Hook Location . . . . . . . . . . . . . . . . .

34

3.2.5

Inuence of Winch Operator Behavior

. . . . . . . . . . . . .

37

3.2.6

Winch Force Inuence

. . . . . . . . . . . . . . . . . . . . . .

38

3.2.7

Inuence of Cable Model . . . . . . . . . . . . . . . . . . . . .

40

3.2.8

Inuence of Cable Drag Coecient

. . . . . . . . . . . . . . .

42

3.2.9

Analysis of Aggressive Pilot Behavior . . . . . . . . . . . . . .

43

. . . . . . . . . . . . . . . . . . . .

4 Summary and Outlook

45

A Coordinate System

46

B User's Guide

48

iv

References

49

List of Figures

1.1

Rear View Study of an ASK 21 Glider during Winch Launch . . . . .

2

1.2

Side View Study of an ASK 21 Glider during Winch Launch

. . . . .

3

1.3

Phases of Winch Launching

. . . . . . . . . . . . . . . . . . . . . . .

4

1.4

Necessary Auxiliary Equipment for Winch Tow Cable . . . . . . . . .

5

2.1

Block Diagram of Simulation . . . . . . . . . . . . . . . . . . . . . . .

7

2.2

Block Diagram of the Glider Model . . . . . . . . . . . . . . . . . . .

9

2.3

Block Diagram of the Winch . . . . . . . . . . . . . . . . . . . . . . .

11

2.4

Characteristic Power Curve

12

2.5

Computer-Rendering of the Cable Model in a Kite Simulation

2.6

Block Diagram of the Cable Model

2.7

Illustration of Forces Acting on the

2.8

Block Diagram of the Winch Operator Model

. . . . . . . . . . . . .

18

2.9

Block Diagram of the Pilot Model . . . . . . . . . . . . . . . . . . . .

20

3.1

Flight Path of the Reference Conguration . . . . . . . . . . . . . . .

26

3.2

Pitch and Climb Angles during Reference Launch

. . . . . . . . . . .

26

3.3

Safety-relevant Parameters during Reference Launch . . . . . . . . . .

27

3.4

Elevator Deection During the Reference Launch

. . . . . . . . . . .

28

3.5

Winch Force during the Reference Launch

. . . . . . . . . . . . . . .

28

3.6

Flight Paths with Varying Cable Types . . . . . . . . . . . . . . . . .

29

3.7

Flight Paths with Variable Tow Distance . . . . . . . . . . . . . . . .

30

3.8

Flight Paths with Acting Steady Winds . . . . . . . . . . . . . . . . .

3.9

Safety-relevant Parameters with

3.10 Angle of Attack during Gusts

. . . . . . . . . . . . . . . . . . . . . . . . . . .

13

. . . . . . . . . . . . . . . . . . .

14

j th

2.5m/s

Discrete Cable Mass

Tailwind

. . . . .

15

31

. . . . . . . . . . .

32

. . . . . . . . . . . . . . . . . . . . . .

33

3.11 Weak Link Force Response after Gust Disturbance

. . . . . . . . . .

33

3.12 Changes in Pitch due to Gusts . . . . . . . . . . . . . . . . . . . . . .

34

3.13 Changes in Pitch due to Tow Hook Location . . . . . . . . . . . . . .

34

3.14 Inuence of CG Hook Location on Flight Path . . . . . . . . . . . . .

35

3.15 Safety-relevant Parameters with CG Hook Moved 3.16 Changes in Pitch due to Operator Behavior

10cm

Aft . . . . . .

36

. . . . . . . . . . . . . .

37

3.17 Safety-relevant Parameters for Nominal Winch Target Force Rate of dFT = 600N/s . . . . . . . . . . . . . . . . . . . . . . . . . . Change dt dFT 3.18 Flight Paths with Varying Target Force Rate of Change . . . . . dt 3.19 Elevator Deection η with Varying Maximum Target Forces FT,max .

37 38 38

3.20 Flight Paths with Varying Maximum Target Force . . . . . . . . . . .

39

FT,max = 13kN

40

3.21 Safety-relevant Parameters for Maximum Target Force

3.22 Inuence of Dierent Physical Cable Models on Flight Path 3.23 Flight Paths with Varying Cable Drag Coecient

v

CD,C

. . . . .

41

. . . . . . . .

42


3.24 Flight Path of Aggressively Flown Winch Launch

. . . . . . . . . . .

3.25 Safety-relevant Parameters during an Aggressive Winch Launch

vi

. . .

43 44

List of Symbols

Notation

A C E F G, H I K L M N P R Re S T V X, Y , Z c d e f g h i j k l m n p r s t p, q , r u, v , w x, y , z

Cross Section Coecient Energy, Modulus of Elasticity Force Transfer Functions Moment of Inertia Control Constant Unstrained Cable Segment Length Mach Number, Moment, Molecular Mass Rotational Speed Power Universal Gas Constant, Location Reynolds Number Safety Margin Time, Temperature, Cable Tension, Torque Velocity Cartesian Forces Strain-Speed-Proportional Stress Coecient Diameter, Distance Unit Vector Power Lever Setting, Frequency Gravitational Acceleration Unit Step Response, Altitude Gear Transmission Ratio Identication Number of Cable Element or Mass Point Scaling Factor Strained Cable Segment Length Mass Number of Cable Elements or Mass Points, Load Factor Air Pressure Relative Location Complex Variable of the Laplace Domain Time Cartesian Rotational Speeds Cartesian Velocities Cartesian Coordinates

continued on next page vii

Chair of Flight Dynamics RWTH Aachen University ∆ Φ Θ Ψ

Dierence

α χ ε γ η λ

Angle of Attack

Bank Angle Pitch Angle Heading

Glider-Winch-Angle Strain Angle of Climb Elevator Deection, Degree of Eciency Angle between Glider's Longitudinal Axis and Cable Force

µ ρ ω

Viscosity Coecient Density Angular Frequency

Indices

0

Initial Value at Beginning of Simulation, Sea-Level Condition

AC C D CS DL E G N NE O P S T V W

Aircraft

a d f g hf i k lf

Aerodynamic Coordinates

Cable Cable Drum, Aerodynamic Drag Camshaft Driveline Winch Engine, External Glider Integrating Time Constant Never Exceed Winch Operator Pilot Stall Target Derivative Time Constant Winch

Delay Time Aircraft-xed Coordinates Geodetic Coordinates Higher Frequency Neuromuscular Derivative Time Track-xed coordinates Lower Frequency

viii


Abbreviations 6DoF

Six Degrees of Freedom

CG

Center of Gravity

Datcom

Data Compendium

FEM

Finite Element Method

IAS

Indicated Airspeed

ICAO

International Civil Aviation Organisation

ISA

International Standard Atmosphere

GUI

Graphical User Interface

Conventions in Mathematical Notation

Z |Z| ~ Z Z Z˙ Z0 Z :=

Scalar Term, Scalar Value of

~ Z

2-Norm of Z Vector Second Order Tensor Derivative of

Z

in Direction of Time

Amplitude Denition of Z

Typeset Conventions

Italicize

Small Caps Typewriter

Name of File and Path from Simulation's Main Directory Action to be taken by the simulation user Name of Simulink Block

ix

Chair of Flight Dynamics RWTH Aachen University 0.1 Foreword This study thesis has been written at the Chair of Flight Dynamics at the RWTH Aachen University as part of a more comprehensive research project pertaining to the behavior of gliders in ight which has been funded by the German Federal Ministry of Transport, Building and Urban Aairs. The primary goal of this thesis is to provide a quantitative analysis of the mechanic loads occurring during the winch launch of a glider and to supply numeric data for future optimization of the winch launch process. This has been attempted to achieve by developing a computer simulation in the environment of MATLAB/Simulink. While the rst half of the written report is intended as documentation of the development process and as a reference manual, the second half uses the presented simulation as a tool for grading and discussing the winch launch. By varying dierent parameters, the inuences of these variations are identied and an attempt is made to compare these results to practical experiences. A project of the magnitude of this simulation is achieved through the helpful input of many dierent people and institutions. At this point I would like to thank everyone who has been involved in this project. Specically, I would like to mention and thank Dipl.-Ing.

Jan Nowack for his tuition of my study thesis and for him

providing the academic guidance needed in the sometimes frustrating, yet often rewarding process of writing this thesis.

Dipl.-Ing.

Andreas Gäb was also very

helpful and always eager to answer my numerous questions about working with MATLAB/Simulink. For many evenings of creative discussion and the opportunity to kick ideas back and forth, I also need to thank cand. phys. Jens Richter. The dierent proof-readers who aided in bringing this thesis into a presentable form are not to be forgotten and deserve their share of praise. Special thanks in this regard go to Kathrin Herkenrath.

At last, a sincere thank you also is extended to the

companies Tost Startwinden GmbH and Rosenberger Tauwerk GmbH for providing information on their products.

Aachen, Germany,

Christoph Santel

in the fall of 2008

1

1 Background

©JM-Fotoservice Figure 1.1: Rear View Study of an ASK 21 Glider during Winch Launch

1.1 Introduction In most parts of western Europe and many other parts of the world, the winch launch is the preferred method of launching gliders.

Its relatively low operating

costs, feasible operator requirements and relatively low complexity have ensured the widespread usage of winches in modern day soaring and provide many glider sites with a reliable and inexpensive method of launch. A basic impression of the winch launch can be gained from the side and rear view studies given in gures 1.1 and 1.2. In comparison to the aerotow launch, where the whole propulsion equipment is airborne and must be designed for acceptable ight performance and maintained according to governing aeronautical regulations, the winch is completely ground based. This makes the use of lightweight design techniques in the construction of a glider winch not compulsory and also alleviates the regular maintenance requirements while using simpler technologies. Also, the operator does not need to be a fully rated pilot for piston-engine airplanes. While the major advancements in glider design - such as the use of composite materials and laminar airfoils - have been driven by competitive considerations, the 2


design of winches lacks such a driving force. With the widespread introduction of composite high performance gliders and the ensuing increase in maximum takeo weight, it has become necessary to equip winches with stronger engines, though the basic technology has changed little since the widespread introduction of winches in the 1950's and 1960's.

Yet, the most recent innovation in this eld has been

the replacement of the steel cables used to tow the gliders by synthetic cables. Completely new drivetrain designs, being powered by electric motors, have been in operation for several years, though most of them are prototypes or proof-of-concept designs. Generally, the technical research in winch launching has been very low-key, providing only little written analysis on the nature of the winch launch. Additionally, it should be mentioned that the few documents which regulate the construction and operation of glider winches, such as the Operational Requirements for Glider and Motorglider Winches (Tec86) of the German Aeroclub, mostly rely on values of experience and rough estimates in their assessment of the acting loads. Even though a previous thesis with similar content has already been treated at the Chair of Flight Dynamics by Kloss (Klo07), the goal of this thesis and simulation is to provide a means of comparison and quantication of aspects pertaining to the winch launch process.

©rheingau-foto.de Figure 1.2: Side View Study of an ASK 21 Glider during Winch Launch

3


1.2 The Winch Launch The winch launch is a highly dynamic method of launching gliders to a suciently safe altitude for free ight. Derek Piggott describes the concept in a simple manner: The basic principle of winch [...] launching is the same as launching a kite. The aircraft is pulled along the ground until it has sucient speed to lift o (Pig96). After lifting o, the glider will then - after having reached a suciently safe altitude - transition to a climb which is characterized by steep pitch and climb angles. As the horizontal distance between the glider and winch decreases, the climb and pitch angles slowly decrease until the cable is either manually or automatically released when the aircraft is in the vicinity of the winch. At this point, the glider should be in nearly steady and horizontal ight. Apel (Ape96) denes six distinct phases of the winch launch which are illustrated in gure 1.3. Specically, these phases are: 1. before ground roll 2. ground roll and lift o 3. transition to climb 4. climb 5. transition to level ight and cable release 6. after cable release

from (Ape96) Figure 1.3: Phases of Winch Launching

The most critical phase is considered to be the transition to the climb, since the aircraft will have a relatively high pitch angle at relatively low altitude. In the event of a cable break, the airspeed will usually decay swiftly. To prevent a stall at low altitude the nose will need to be quickly lowered in order to prevent the airspeed from falling below the stall speed. 4


For reasons discussed later, only phases 3 through 5 are accurately depicted in the developed simulation.

The simulation terminates at the moment of cable release,

1

and does not regard free ight .

1.3 Necessary Equipment The cable is connected to the glider through a hook. During aerotow the tow cable is usually attached as far forward of the aircraft's center of gravity (CG) as possible. This increases static lateral and longitudinal stability and relieves pilot workload. However, high longitudinal stability is uncalled-for during the winch launch.

It

would prevent the high pitch and climb angles used to gain altitude quickly and mounting the tow hook close to the CG becomes necessary. Most modern gliders are equipped with both, a nose hook for aerotows as well as a CG hook for ground launches. Additionally, several safety components are required by the German Glider Operation Regulations (Seg03). They are depicted in gure 1.4 and need to be mounted in the following order at the end of the cable closest to the glider:

standardized tow ring

leading cable, enshrouded in a sti hose to prevent loops from forming

weak link, according to aircraft ight manual

intermediate cable

drag chute

clipper hook, for quick disconnection of auxiliary cable equipment

main cable

tow rings

leading cable

weak link

intermediate cable

drag chute

clipper hook main cable from (Mai93)

Figure 1.4: Necessary Auxiliary Equipment for Winch Tow Cable

1.4 Development Considerations The numeric nature of this thesis makes it necessary to analyze a specic winch and glider combination. This contrasts the highly generic value of an analytical analysis which is often independent of specic equipment. To provide signicant results, the analyzed aircraft and winch need to be suciently generic in their nature. Therefore,

1 phase 6 of the winch launch 5


the ASK 21 primary training glider, developed by Alexander Schleicher GmbH & Co. Segelugzeugbau of Poppenhausen, Germany, was chosen as the simulated glider. The ASK 21 is a composite two-seat training glider in widespread use worldwide and its aerodynamics and ight performance are similar to other aircraft of the composite primary training eet. For the purpose of this simulation, the ASK 21 is said to be representative of this eet. Also, the availability of a ight mechanics model, drawn from previous research of the ASK 21 at the Chair of Flight Dynamics, was a factor in selecting this glider type. While data for a specic aircraft - the ASK 21 - was readily available, few specics on certain winch models were at hand.

Through the generous assistance of Tost

Startwinden GmbH of Assling, Germany, it was possible to obtain technical data on one of the company's winch types. Yet many parameters still had to be estimated. Though Tost is one of the market leaders in the construction of glider winches, many winches in operation in Germany and worldwide are self-constructed singleunit productions. This causes the general validity of the winch model to be lower than the glider model. The cable and glider are both moving through space during the simulated winch launch, whereas the winch is considered to remain stationary. Hence, the cable and gliders are both modeled with six degrees of freedom (6DoF) in cartesian space using the principles of Newtonian mechanics. But the full expressiveness of the 6DoF could not be exhausted. Time restrictions to this thesis allowed only for an implementation of a basic pilot model and control law that controls only the aircraft's longitudinal motion. This causes all following simulations to be of a symmetric nature and the following analysis of the winch launch to be valid on the presumption of quasitwo-dimensionality.

In the future, the inclusion of control laws to inuence the

aircraft's lateral movement is possible and would utilize the possibilities of the 6DoF simulation more comprehensively. The author would welcome any such additions in the future.

1.5 Simulation Environment in MATLAB/Simulink The portrayed models have been implemented using the R2007b version of MATLAB, created and distributed by the The MathWorks Inc. of Natick, Massachusetts, USA. This is an object-oriented programming language and development environment with focus on vectorial and matrix calculations. One of MATLAB's tools is Simulink. It allows for the graphical denition of mathematical models analogous to block diagrams. The individual elements of such models, called blocks, interact through signals with each other. Capabilities such as the ability to dene transfer functions in the Laplace complex variable domain and the possibility of using embedded MATLAB code make Simulink a tting tool for control engineering modeling and numeric ight simulation. For the standard calculations of ight simulation, the Chair of Flight Dynamics has developed a library of commonly used MATLAB/Simulink blocks.

Tasks

executed by this library might include coordinate transformations, calculation of aircraft inertia, determination of international standard atmosphere values and so forth.

This MATLAB/Simulink library proves an adequate basis for this study

thesis. 6

2 Models and Simulation For the purpose of this simulation the problem of the glider winch launch has been broken down into three interfaced primary components - winch, cable and glider which interact through their states with each other. In order to depict the inuence of human operators on winch and aircraft and to achieve closed loop control circuits over these primary components, rudimentary pilot and winch operator models are integrated as feedback loops.

This interaction of the ve independent models is

depicted in block diagram 2.1. Methods regarding standard atmospheric inuence are integrated into the relevant models, making the International Standard Atmosphere (ISA) the sixth used in this simulation. The dierent natures of the physical phenomena within each model make the use of dierent coordinate systems reasonable. A description of each of the used systems is given in appendix A. Appendix B provides a user's guide for easier handling of the simulation by the end user.

Winch Launch Simulation Chair for Flight Dynamics RWTH Aachen

66{101}

Glider State Cable Force (g) [ N]

Drawn Power [W] Winch Force [N]

3

Cable Force (g) [ N]

Rendered Power [W]

Winch Force [N]

Operator Throttle

Glider State

eta_Pilot [rad]

66{101}

Cable Model Winch

Glider

Winch Force [N]

Glider State

eta_Pilot [rad]

66{101}

Operator Throttle

Glider Pilot Glider State

66{101}

Winch Operator

Figure 2.1: Block Diagram of Simulation

From a developmental standpoint, this simulation is the enhancement of a generic six degrees of freedom (6DoF) ight simulation in MATLAB/Simulink which has been previously developed at the Chair of Flight Dynamics (Gäb07). Several blocks regarding the peculiarities of the winch launch were added to the existing aircraft model, which was then integrated into the rest of the simulation. This facilitated the use of an existing graphical user interface previously intended for the generic aircraft simulation.

7


2.1 Implemented MATLAB/Simulink Blocks

2.1.1 Aircraft Model The used generic MATLAB/Simulink aircraft model, which for the purpose of this simulation has been integrated into the

Glider block, is further divided into several

blocks; one each for calculation of acting forces and moments, the 6DoF equations of motion, terminating conditions, events, calculation of wind, and blocks for modifying the glider's state data bus with wind information and adding current ISA values to the bus. The aerodynamic and inertial data of the Schleicher ASK 21, which has been drawn from previous research projects at the Chair of Flight Dynamics, is stored in the les

ask21aero_edited.mat

and

ask21_moi.mat

respectively.

Through the use of nonlinear coecients the aerodynamic moments and forces acting on the aircraft are calculated.

The used model is limited in that it only

regards an obstruction-free quasi-static airstream around the aircraft. This causes the aircraft's behavior during the phases of ight in which it is exposed to strong ground eect - namely the take-o accurately.

1 run in this simulation - not to be depicted

As soon as the virtual glider reaches its initial climb attitude and an

altitude of approximately one wingspan above ground level, the aerodynamic results are said to be within acceptable accuracy. The aerodynamic forces and moments, along with the forces and moments induced into the glider by the winch cable are then passed to the aircraft's rigid body inertial model. This, again, is in accordance with the conventional approaches of basic ight dynamics in which the aircraft is dened as a point mass. Its translational inertia is regarded by the aircraft mass inertial tensor

I AC .

mAC

and its rotational inertia is depicted in an

These parameters are interfaced with the glider's state through

the Newtonian basic equations of motion, as can be drawn from Alles (All05) or Brockhaus (Bro01). One of the shortcomings of the rigid body model is that it does not regard aeroelastic eects. Especially when high load factors are present - as is the fact during the main climb phase - the validity of this assumption has to be challenged. The bending of the wing is inuenced by the wing's geometric moment of inertia, the wingspan and load factor. This results in large displacement of the wing's centerline, especially in open class gliders. But the deformations in primary training gliders are usually smaller and not considered for our purposes. A further assumption is that the quasi-static, undisturbed airow around the aircraft is said to be incompressible. All occurring airspeeds in the simulation are

VN E = 280km/h MN E = 0.23. As is

expected to be smaller than the ASK 21's

IAS (Ale80), being

equivalent under standard conditions to

general practice for

M < MN E < 0.3, the compressibility eects are considered to be of small magnitude and negligible.

Aircraft Model Modications The generic aircraft model - which is taken from previous work at the Chair of Flight Dynamics - needs to be modied to regard the specics of the winch launch. Block

1 phase 2 of the winch launch 8


diagram 2.2 illustrates this. The original aircraft model has not been designed to regard acting external forces, except aerodynamic lift and drag, thrust and gravity. Yet, the force being exerted by the tow cable onto the glider is the primary mean of increasing the glider's sum of potential and kinetic energy. It is self-evident that

Cable Load Interface is located in the Glider model's External Forces and Moments block.

an interface for the cable-induced loads has to be introduced.

This

3

1

Cable Force (g) [N]

xi _rad

Ground 1 2

eta _Pilot [rad ] eta [ rad ] 4 {4}

eta _Pilot [rad] Mechanical Limit on Flight Controls Movement

zeta _rad

Ground 2 throttle _norm

Ground 3 Clock

30 {49 }

Time

fcn Wind

3 Aircraft Loc . ( g)

3

Cable Force

3

Forces [N ]

(g) [ N ]

3

Forces [N ]

Location

Wind Influence

3

Wind

30 {49 }

30 {49 }

Glider State

time -dep . Wind 13 {13 }

Wind

Moments [ Nm ]

Control Inputs

4 {4}

3

Moments [ Nm ]

Glider State Out

Wind Calculation 30 {49 }

60 {95 }

Out

In

66 {101 }

Aerodynamic Forces

Glider State

66 {101 }

In

(X, Y , Z )^(T)_(a) [ N ]

External Forces and Moments

3

Eq . of Motion 6DoF,Quaternions

3

Aero . Forces (X, Y , Z )^(T)_(a) [ N ]

ISA

Rendered Power

Add Wind

66 {101 }

1

[W ]

Glider State

Rendered Power [W]

Determination of Rendered Aircraft Power 2

66 {101 }

Glider State Glider State

66 {101 }

Events State

66 {101 }

Cable Force

3

(g) [ N ]

Terminating Conditions

Figure 2.2: Block Diagram of the Glider Model The force

F~G,C

induced from the cable into the glider is passed into the interface,

which then calculates the resulting moment

~ CG-Hook R ~ hook, MG,C follows to ~ G,C = R ~ CG-Hook × F~G,C M

center of gravity. With

F~G,C

and

~ G,C M

~ G,C M

of

F~G,C

force around the glider's

being the location vector of the glider's CG tow

(2.1)

are then added to the aerodynamic and gravitational loads of the

generic model and the respective sums are passed into the inertial calculations. As the input loads into the generic model's inertial calculations are formulated in aircraft-xed coordinates, and as

F~C,G

Cable block in geodetic ~ CG-Hook is also most necessary. R

is given by the

coordinates, a coordinate transformation becomes easily formulated in aircraft-xed coordinates.

To properly declare the termination of the simulation at the moment of cable

2 , an additional terminating method

Cable Release Mechanism devised and integrated into the glider's Terminating Conditions block. release

has to be The ASK

21 uses a standard CG tow hook supplied by Tost GmbH Fluggerätebau of Munich, Germany. This hook releases the cable automatically when the force

λRelease

to the

being the

~xf FG,C,z

critical angle and

FG,C,z

F~G,C

exceeds a

~xf -axis in the aircraft's plane of symmetry. With FG,C,x and ~ zf -components of F~G,C , the cable angle λ follows to

λ = sin−1 q 2 2 FG,C,x + FG,C,z

(2.2)

2 transition from phase 5 to phase 6 of winch launch according to Apel (Ape96) 9


The method terminates the simulation as soon

λ > λRelease

and ensures that no

termination occurs if no cable-induced force is present. Due to the elastic nature of the cable model used, cable vibration might occur. In the case that the winch-induced tension has not yet properly engaged end of the tow cable, forces of extremely small magnitude exist. To prevent a termination of the simulation,

4 with

~G,C all F

3 at the glider

λ > λRelease might with FG,C < FG,C,min are 5

treated as if no cable induced force were present at the release mechanism . The pilot-commanded elevator deection

ηP

might dier from the actual elevator

η due to restricted movement of the ight controls. This is described in Mechanical Limit on Flight Controls Movement by linking the signal ηP with η through a saturation block to ensure that η ∈ [ηmin , ηmax ]. The block Calculation of Rendered Aircraft Power determines the currently rendered power PAC by the aircraft. Power is rendered by the aircraft's movement deection

the block

through the geopotential eld (subscript pot ), its changes in its kinetic state (subscript kin ) as well as through aerodynamic drag (subscript D ):

PAC = Ppot + PD + Pkin

(2.3)

Ppot = −mAC · ~g · ~vAC PD = −~vAC · F~D 1 d 1 mAC · ~vAC · ~vAC + ω ~ AC · (I AC ω ~ AC ) Pkin = dt 2 2

(2.4)

with

(2.5) (2.6) (2.7)

and



ω ~ AC

 p :=  q  r AC

(2.8)

To clarify the sign convention, it should be stated that an increase in an energetic state of the glider carries with it

P > 0.

In order to exploit the specic advantages of each coordinate system, dierent systems are used to calculate the dierent power components. geodetic (g ),

PD

in aerodynamic (a ) and

Pkin

Ppot

is determined in

in aircraft-xed (f ) coordinates. The

winch

block for further

Wind acting on the glider in ight is easily determined using the

Wind Influence

rendered aircraft power

PAC

will later be parsed into the

calculations. block. It utilizes a vectorial method allocated in the le

WindVectorField.m, allow-

ing for the denition of wind vector elds varying in time and location. As previously mentioned in section 1.4 and described in more detail in section 2.1.4, only longitudinal motion of the glider is controlled by the pilot model. This forces a disregard of the yawing and pitching moments produced by mounting the

3 For further discussion of numeric engagement of the cable solution, refer to section 2.3. 4 in the order of 10−9 N

5 This could be physically interpreted as friction keeping the ring engaged in the tow hook when only minor a tow force

F~G,C

acts on the glider.

10


CG tow hook out of the aircraft's plane of symmetry. To achieve this properly in the later studied cases, the be set to

~yCG-Hook,f -component of CG hook's location vector must

~yCG-Hook,f = 0.

2.1.2 Winch Model Though having been treated theoretically by Riddell (Rid98), the modeling of inertial eects on the winch during the launch could not be found in previous numeric simulations. For example, the works of the Akaieg Karlsruhe (HS98) as well previous research at the Chair of Flight Dynamics by Kloss (Klo07) have modeled the winch solely as a source of a time-variant torque and force acting upon the tow cable. With the creation of this winch model, an attempt has been made to provide a generic, yet signicant physical model. It allows for signal feedback routings pertaining to the inuence of the cable and glider upon the winch as well as the addition of a winch controller model. Camshaft Rotational Acceleration [ rad / s^2]

-K-

1/(Drive Train MoI ) [m ^2/kg], Reduced to Camshaft

-CInitial Throttle Setting 1 2 Operator Throttle

den (s) Throttle movement mechanically limited

Add Delay Function

1 Drawn Power [W]

1 s Integrator

1-D T (u) Camshaft Angular Frequency [rad /s]

-K[rad /s] -> [RPM ]

Camshaft Rot . Speed [RPM ]

-K-

Avail . Engine Power [W ]

[kW] -> [W]

Product

Engine Power Output [W ]

Characteristic Engine Diagram N_CS [RPM ] -> P_max [kW]

-K-

Drum Roational Speed

-K-

Drum Driving Power

[W ]

mech . Degree of Efficiency

Subtract

[ Rad /s ]

Divide

1/Gear Transmission Ratio

Drum Driving Torque [ Nm ]

-K1/Drum Radius [1/m ]

1 Winch Force [N]

Figure 2.3: Block Diagram of the Winch Using the methods of automotive engineering as presented by Kiencke and Nielsen (KN00), the winch is represented by a driveline and engine model.

The winch

model's block diagram is given in gure 2.3. As previously discussed, the design of winches often varies. The most prominent variations are in the used engine - being either operated on gasoline or diesel fuel - as well as the use of a torque converter, or lack thereof, in the driveline.

Due to the availability of data, it was decided

to represent a driveline without torque converter being powered by a supercharged diesel engine.

The driveline itself is said to consist only of the following rotating

elements: the camshaft, an ideal gearbox, one cable drum and a shaft connecting the cable drum to the gearbox.

These components are said to be sti to torque.

Mechanical losses of all elements are regarded in one driveline degree of eciency

ηDL

while the inertial behavior is regarded in one scalar driveline moment of inertia

reduced onto the engine camshaft

IDL, red .

Though intended as a model of a two

drum winch, the second cable drum is not regarded since in normal operation only one drum is engaged to the drivetrain using a clutch. The centerpiece of the winch simulation is the engine's characteristic diagram providing a correspondence between the engine crankshaft's revolving speed 11

NCS


and the maximum power output

PE, max (NCS ).

This diagram, given in gure 2.4, has

been implemented into a lookup table using cubic spline interpolation between nodes to provide a continuously dierentiable power output over time.

For operations

outside the data interval provided, cubic spline extrapolation is used. A result of this extrapolation is that the engine output power rapidly declines when the engine is being operated above the camshaft revolving speed for maximum power The same is true for moving operations into relatively low crankshaft speeds.

These eects

coincide with actual observations of internal combustion engines.

Data Source: (Gen08) Figure 2.4: Characteristic Power Curve Tost Startwinden GmbH kindly provided information on its Series 010 winches as well as the GM V8 454 gasoline engine used in this product. Unfortunately, during the development of the winch model, this engine proved to be inadequate. It lacks the torque necessary for the analysis of higher winch forces in section 3.2.6 and made the implementation of a higher torque diesel engine necessary. The GM Duromax Diesel 6.6L turbocharged diesel engine was chosen, which is used in the Skylaunch 3 winch (Sky08) produced by Skylaunch Ltd of Shropshire, Great Britain. Though data on the basic engine performance was obtained though General Motors (Gen08) no quantitative correlation between engine throttle setting and the engine's actual power output was given. Therefore, the throttle inuence

f

has been approximated

to be a linear scaling factor of the maximum power output, reducing it to the actual engine power output. To account for the slight delay in availability of engine power following a change in the throttle setting, the linear scaling factor is adjusted through a rst order delay element with a relatively short derivative time. The actual throttle setting is determined by ltering the operator commanded throttle setting through a saturation block so that

f ∈ [fmin , fmax ] = [fmin , 1].

The upper limit of the block

is set to allow full throttle operation and the lower limit is selected to approximate idle operation. 12


The engine output power, adjusted for mechanical losses along the driveline

ηDL , as well as the camshaft rotational speed ωCS , the gear transmission ratio i and drum diameters dd are then used to determine the scalar force FC,W exerted by the winch onto the cable. Also, power dierence through a constant degree of eciency

between the engine output power and the power drawn by other simulation components

PE − PDrawn

is said to accelerate the driveline's revolving speed, causing a

feedback loop within the winch driveline. The data provided by Tost Startwinden was limited to the cable drum diameter and gear transmission ratio of its Series 010 winches and little other quantitative information on winch properties was found.

This made it necessary to estimate

many properties, such as mechanical degrees of eciency, moments of inertia of the driveline, or inuence of the buttery valve setting on the engine.

A more

general winch model, lacking the specics of a certain winch type, is the result of these approximations and use of values of experience. In comparison to the aircraft model, which is considered a precise enough representation of the Schleicher ASK 21, the winch model cannot be said to represent one specic type. It should much rather be interpreted as being similar to many of the winches with two cable drums in operation today.

2.1.3 Cable Model A detailed description of the tow cable's deformation is necessary to accurately determine the cable tow force

F~G,C

acting on the glider. Due to the non-conservative

nature of the aerodynamic forces acting on the cable, in addition to the conservative gravitational inuence, it was decided to model the cable by the means of a dynamic

Finite Element Method (FEM ).

from (WLO07) Figure 2.5: Computer-Rendering of the Cable Model in a Kite Simulation

The model - placed in the

Cable Model

block - is based upon the works of

Williams, Lansdorp and Ockels (WLO07) and has been originally developed for the simulation of tethered kites in electric power generation through a laddermill. 13


Figure 2.5 shows a computer-rendering of the deformed cable in Williams', Lansdorp's and Ockels' kite simulation. Due to the high dynamic similarity between a tethered kite - which in a laddermill is reeled in and out at low frequency - and a glider being launched, this model is adequate. Though Williams, Lansdorp and Ockels (WLO07) present an inelastic model, provisions are already made to easily include elastic calculations. Due to this, the cable tension is modeled as being of damped linear elastic nature using a variation of Hooke's law together with a damping term. The block diagram of the cable model as it is implemented in this thesis is given in gure 2.6.

[20x3]

-C-

GroundMatrix

Node Dynamics

n

5{260}

Ground Matrix t

Clock -C-

Reeling Unit

n_0 n

n_0 n

1

5{260}

[20x3]

R

[20x3]

R_dot

[20x3]

r

[20x3] 20

R_dotdot

66{101}

[20x3] Glider State

Glider State

Node Dynamics

5{260}

R_dotdot

Boundary Conditions and Integration

r_dot

l_dot

fcn 2

WinchForce

Winch Force [N] -C-

3

WinchLocation

WinchLocation -C-

g

g -C-

d_cable

d_cable -C-

E_cable

3

1 Cable Force (g) [N]

E_cable -C-

c_cable

c_cable -C-

C_d_cable

C_d_cable 20 -CL_cable 20 -Cm_cable

CableForce

L_cable

m_cable

Determine Node Acceleration

Figure 2.6: Block Diagram of the Cable Model

As a leading note:

To facilitate references to Williams, Lansdorp and Ockels

(WLO07) more easily, it has been decided to adopt the nomenclature and symbols used by them for the description of the cable model. It might dier slightly from the nomenclature of the remaining sections. At the beginning of the simulation, the cable is discretized into

n0

discrete masses

interconnected by massless elastic cylinders. Enumeration starts with the mass point closest to the glider and increases on its way to the winch. The iterative variable is used to identify parameters pertaining to the cylinder between the

j

and

j + 1th

j th

j

lumped mass as well as to the

masses.

The free cable length and the closely related free cable mass vary in time since the cable is reeled onto the winch drum during the launch. Whereas

n is the current

nth mass is removed when the segment length ln between the last cable element and the winch falls below a predetermined length lmin = k ∗ · lref . In this case k ∗ is a scaling factor for an arbitrary reference length lref . number of discrete mass points, the

This mathematical representation of reeling the cable onto the drum is represented in the

Reeling Unit

block. 14


The acceleration of each mass point is dependent upon the sum of internal and external forces acting on it. block

Because of this, the embedded MATLAB function

Determine Node Acceleration

calculates the total acceleration acting on

each cable mass point in geodetic coordinates by determining each of the acting internal and external forces at each mass point. These forces are then determined via methods stored in further

.m -les.

External forces, namely aerodynamic drag and gravity, are modeled in direct accordance with Williams, Lansdorp and Ockels (WLO07). The presented algorithms for the calculation of each of the external forces have been placed in the and

CableGravity.m

CableDrag.m

les respectively. For the specics of the determination of the

external forces, it is deemed appropriate to point the reader to (WLO07), as this section has been adopted precisely as described. As mentioned before, the internal forces are determined through a damped linear elastic model, the respective method being accessible within the

CableTension.m

le. Dietz and Mupende (DM04) use a similar model when analyzing the interaction between synthetic cables and winch drums.

Figure 2.7: Illustration of Forces Acting on the

The magnitude of the tension

Tj

in the

j th

j th

Discrete Cable Mass

cable element is easily found by using

a damped form of Hooke's law;

Tj = Ac · Ec · εj + | {z } linear elastic term

whereas element.

A · c · ε˙ | c {zc }j

= Ac (Ec · εj + cc · ε˙j )

(2.9)

linear damping term

Ac is the cable cross section and εj is the strain experienced by the j th Ec is the cable's modulus of elasticity and cc is a strain-speed-proportional

cable stress coecient. The cable cross section is directly related to the cable diπ ameter dc by Ac = · d2c while cross section contraction due to strain is neglected 4 because of the braided nature of cables. By also relating the j th element strain εj to the respective strained and unstrained lengths lj and 15

Lj

of the element, the tension


magnitude can be expressed as

" # π 2 lj l˙j Tj = · dc · Ec · − 1 + cc · 4 Lj Lj

(2.10)

As perfect exibility is assumed in the cable, only axial tension forces can be trans-

axial

T~j

j th segment is easily oriented by using the ~j is orientation of the j th cable element. The oriented tension force T " # ˙j l l π j − 1 + cc · · ~ej (2.11) T~j = Tj · ~ej = · d2c · Ec · 4 Lj Lj

mitted, the tension force

with the unit vector

~ej

acting in the

describing the orientation of the

j -th

cable element.

1 ~ 1 ~ ~ej = · ~rj = · Rj − Rj+1 lj lj

(2.12)

Taking the results from the methods of the

CableDrag.m, CableGravity.m and Ca-

bleTension.m les, the ensuing cable dynamics are determined within the Determine Node Acceleration block as follows. mj is said to be

The total force

F~j

acting on the

F~j = F~E,j + T~j−1 − T~j if

F~E,j

(2.13)

is the sum of all external forces acting upon the

the mass point acceleration

~¨ j R

j th

mass point. Therefore,

trivially follows as

~¨ j = 1 F~j R mj The temporal integrals

j th mass point

(2.14)

~˙ j R

and

~ j, R

of course, are the speed and location of the

j th

mass point. Equation 2.13 is also illustrated in gure 2.7. To properly depict the glider launch within the cable model, several boundary conditions must be regarded: 1. The location of the rst cable mass point at of the glider's CG tow hook.

j=1

is identical to the location

This is of course also true for the relevant

derivatives.

~1 = R ~ CG-Hook R ~˙ 1 = R ~˙ CG-Hook R ~¨ 1 = R ~¨ CG-Hook R

(2.15) (2.16) (2.17) (2.18)

2. Since the rst mass point

m1

and the glider's CG tow hook are kinematically

identical, the total force acting onto the rst mass point is in fact the cable force acting onto the glider.

F~G,C = F~1

(2.19) 16


3. The magnitude of the tension winch (j

= n)

Tn

acting onto the cable element closest to the

is dened by the magnitude of the force

FC,W

that is exerted

by the winch onto the cable.

Tn = FC,W ⇒ T~n = FC,W · ~en

(2.20)

As of now, the basic cable properties such as mean cable density

dc ,

modulus of elasticity

Ec

and drag coecient

CD,C

ρc , cable diameter

are kept constant across the

length of the cable. In practice, this assumption is deeply violated by the placement of a drag chute and other auxiliary equipment between the actual tow cable and the glider CG hook. Due to the much higher drag per unit length acting on the drag chute - even in its collapsed form during the actual launch process - the glider end of the cable in practice is expected to deect further against the direction of ight than the numeric results presented here. In the future, an incorporation of varying the above mentioned cable parameters over the cable length can be thought possible. Another source of errors is the behavior of the cable model during the ground

6

roll and initial climb phases of the winch launch . The actual cable will be dragged over the surface of the aireld which is not implemented into the simulation. This causes the actual cable to experience a further friction force oriented against the direction of movement as long as is in contact with the ground and an additional force compensating the eects of gravity. Both of these forces are not regarded in the simulation and therefore limit its accuracy to the time after all of the cable is

7

fully airborne . Currently, the power rendered by the cable is also neglected. It is assumed that the kinetic and potential energies of the glider as well as the aerodynamic dissipation power of the glider are of much greater magnitude than those equivalent conservative and dissipating powers induced by the cable movement. The same is also assumed for the changes in internal elastic energy of the cable. As a nal note on cable models: Etkin (Etk98) has treated the motion of a cable in a similar manner as presented by Williams, Lansdorp and Ockels (WLO07). But he concentrates on the source and description of instabilities created by the cable motion. For the numeric results, it was necessary to choose a particular cable for the reference simulation settings in section 3.1.1. A synthetic cable is chosen in the reference case, because lately these have often displaced the previously used steel cables on glider winches. Rosenberger Tauwerk GmbH of Lichtenberg, Germany, kindly provided data on its Liros-series of synthetic winch cables, which is implemented in the reference cable model.

2.1.4 Human Controller Models Winch Operator Model The purpose of the winch operator model is to stabilize the winch force onto the tow cable around a given target force

FT .

FC,W

exerted

In order to achieve this goal, the

winch operator has been modeled to act as a compensatory single-loop controller,

6 phases 2 and 3 7 This usually occurs in Apel's phase 3 of the winch launch (Ape96). 17


adjusting the winch's throttle in an attempt to stabilize the aforementioned force. It is presumed that operating the winch is a similar task to the longitudinal speed control of a motor vehicle.

Kiencke and Nielsen state that in automotive control

modeling, human driver behavior is often modelled as that of a PID controller (KN00). These assumptions allow the winch operator to be modelled as a PID controller. The controller's transfer function follows to

1 fO (s) = Kf F · (1 + + TV,f F · s) FC,W (s) − FT (s) TN,f F · s

Gf F (s) =

(2.21)

with the input term being the dierence between the winch force and target force

FC,W − FT . As output term acts fO . The straightforward nature of

the winch operator commanded throttle setting the winch operator model becomes evident in its

block diagram 2.8. 1 -K-

Winch Force [N] 2

Subtract

66{101}

K_fF

Glider State Target Force [N]

1

PID

den (s)

Glider State

1

To

PID Winch Neuronal Influence Operator Controller

Variable Time Delay

Operator Throttle

-C-

Time -Variant Target Force

Operator Delay Time [s]

Figure 2.8: Block Diagram of the Winch Operator Model Since excessive forces acting onto the glider at the beginning of the launch might bring the aircraft into a dicult to control state for the pilot, the winch operator will usually gradually increase winch power. Due to this, the target force is not a static parameter, but rather time-dependent.

Through the use of ramp, saturation and

rst order delay elements, a function has been dened which increases the target force from an initial value target force

FT,0

in a continuously dierentiable manner to a nal

FT,max .

The slope of the used ramp-function denes the nominal rate of dFT change of the target force . dT A winch operator will usually decrease the throttle setting as the glider approaches its cable release point to lower wear on material. To allow for this, the actual target force is determined by multiplying the previously described dierentiable target force function with the cosine angle

χ

cos (χ)

of the glider-winch-angle. The glider-winch-

is dened as being the angle between the location vector of the glider's

8

initial location

(~xAC − ~xW ),

(−~xW )

as seen from the winch and the glider's current position

also seen from the winch.

χ := (−~xW ) ∠ (~xAC − ~xW ) Using the law of cosines,

χ = cos−1

χ

(2.22)

follows to

|−~xW |2 + |~xAC − ~xW |2 − |~xAC |2 2 · |−~xW | · |~xAC − ~xW |

For simplication, the calculation of and its multiplication with

Target Force

cos (χ)

χ

! (2.23)

and the dierentiable target force function

are all implemented within the

block.

8 This is the origin of the geodetic coordinate system. 18

Time-Variant


It should be mentioned that modelling the winch operator as a force controller is only a rough rst-order approximation. The force exerted onto the cable by the winch is usually not directly obvious to the winch operator. An actual operator will usually regard multiple other inuences such as cable sag, engine noise and vibration,

9

camshaft revolution speed and wind .

All of these inuences, together with the

operator's experience will determine his actions on the throttle.

It appears that

winch operation could best be modeled through fuzzy logic, as is recommended by Henning and Kutscha (HK03). However, the winch operator model presented above will provide suciently smooth force transitions for the purpose of this simulation and is taken to be acceptable. As a closing note on the subject of winch operators, several assistance systems need to be mentioned. At the Leverkusen aireld in Germany (ICAO-Code: EDKL), Dipl.-Ing.

Markus Pottho of the Luftsportclub Bayer Leverkusen has exper-

imented with the club's winch by installing resistance straining gauges near the drums.

With these, he was able to determine the winch's deformation near the

drum suspension and experimentally determine the reaction force exerted by the cable onto the winch. These measurements were then provided to the operator in visual and audible form via electronics. This system allows for the feedback of the winch force to the operator and closes the control loop in a similar manner to the above mentioned winch operator model.

Yet, the system has not gone past the

experimental stadium. The Wilhelm Nosbüsch GmbH of Haan/Rheinland, Germany, oers a telemetry system as an alternative operator assistance setup (Wil07).

It informs the winch

operator of the glider's airspeed by measuring the dynamic pressure electronically and transmitting it to a winch-side receiver. The data is then processed and passed to a display, being easily accessible to the operator. Though oered commercially, this system is not in widespread use either.

Pilot Model As previously mentioned, the time constraints to this thesis allowed only for a simple pilot model controlling the longitudinal motion. control laws an elevator deection

ηP

Through several superpositioned

is commanded. This control structure becomes

obvious in the pilot model's block diagram 2.9.

Yet, all other pilot inputs into

existing ight controls, such as ailerons, speed brakes, or rudder, are not considered. Quite similar to the winch operator model, the pilot model's goal is to stabilize

10

the glider around a target dynamic pressure

pdyn,T .

At the same time, the pilot

serves in the roll of a pitch damper to lessen or to suppress the glider's phugoid motion. Dynamic pressure / airspeed control is achieved with the

IAS Controller block,

which in turn is being governed by the transfer function of a PID controller:

Gη,pdyn (s) =

1 ηIAS (s) = Kηpdyn · (1 + + TV,ηpdyn · s) pdyn (s) − pdyn,T TN,ηpdyn · s

(2.24)

9 The wind, and especially its variations in intensity, is often challenging to gauge for the winch operator.

10 Recall that for incompressible calculations the IAS is a representation of the dynamic pressure. 19


Here the target dynamic pressure

pdyn,T

is - in contrast to the target tow force

FT (t)

- independent of time. Parallel to the

IAS Controller,

a simple pitch damper is placed for modifying

the aircraft's dynamic behavior. This is realized with a simple proportional transfer function.

Gηq (s) =

ηq (s) = Kηq qAC (s)

(2.25)

A problem which arises with pure IAS control in the manner described is that the pilot would command the aircraft to climb at excessive angles of pitch at low altitude.

Most ight training curricula strongly discourage such a maneuver, due

to the insucient recovery altitude available in the event of a cable break at low altitude. It is more typical for a pilot to leave the ight controls near a trimmed neutral position during initial climb and only to make minor adjustments in pitch and pitch speed.

Only once a perceived safety altitude is reached, the pilot then

transitions into controlling airspeed.

-K-

1

66{101}

Dynamic Pressure

Glider State

eta_q

K_eta _q

1

eta_IAS [rad] z_g

den (s)

Add Product

IAS Controller fade signal

z_g

1

To

Neuronal Influence

Variable Time Delay

eta _Pilot [rad]

-C-

Fading Unit

Pilot Delay Time

[s]

Figure 2.9: Block Diagram of the Pilot Model

To emulate this behavior, the sum of the

IAS controller and pitch damper is Fading Unit block consists of

multiplied with the output of a fading function. This

a non-oscillating second-order delay element, experiencing a unit-step input in the moment the aircraft passes a predetermined safety altitude

hSafety .

The unit step

response of this second-order delay element

( hSafety (t) =

0

Safety −t

t

1−

is the output of the altitude is reached.

1 (T1 T1 +T2

·e

T1

Safety −t

t

− T2 · e

Fading Unit block. tSafety is T1 and T2 are characteristic

T2

t < tSafety ) t ≥ tSafety

∈ [0, 1)

(2.26)

the moment at which the safety times of the second order delay

element. The given signal routing makes certain that ight control inputs, except for a trim deection

ηTrim ,

are suppressed at low altitudes. Due to the location of the CG tow

hook and the resulting moment

~ G,C M

induced by the cable force

F~G,C ,

the aircraft

will gently pitch up during the early climb phase. Additional airspeed control and pitch damping will be faded online only once a safety altitude is reached, steepening the climb angle.

20


Comments on Human Controller Models Through his research in human-machine interfaces, Johannsen (Joh93) recommends augmenting human commanded actions with an additional transfer function to regard neuromuscular rst order delays, psychological anticipation and delay times. For this reason, the transfer function

H(s) =

1 · eTd ·s 1 + Ti · s

(2.27)

has been added to the winch operator as well as pilot models. The eects of this transfer function is minor in comparison to the transfer function of the PID controller representing the human decision process, though a slight eect on the stability of the controlled systems remains. Also, Alles (All80) regards the human inuences in a similar manner. Human controller models of the presented type are very rudimentary in comparison to the complexity of the human decision making process involved in controlling technical processes.

The multitude of inuences on human behavior is still often

dicult to regard adequately for cybernetic consideration. Especially in regard to the fact that the three-dimensional control of a glider in a winch launch - with all available ight control surfaces - is a high work load situation for the pilot which demands his or her utmost attention, the presented PID model is very basic. The prognosis of the control parameters in human controller models, such as control factors, derivative and integrating times, is equally challenging. These parameters have been determined manually by operating each controller (winch operator and pilot) at rst in an unstable, oscillating manner and then iteratively adjusting the parameters to stabilize the controller. This operation in the vicinity of the stability limit is assumed to regard the human decision process accurately enough.

2.1.5 Atmospheric Model / Wind Inuence In order to provide the calculated data in a compatible format with other aeronautical research, the atmospheric inuence has been modeled in accordance with the ICAO's International Standard Atmosphere. At the beginning of the simulation, the aircraft is initialized at sea level, where standard atmospheric conditions prevail. Even though the original generic aircraft model had interfaces for either timedependent or location-dependent winds and gusts, these provisions were deactivated and ignored.

This renders the original GUI inputs for wind non-operational and

prevents accidental numeric contamination of the input data. In the current simulation, a time- and location-dependent three-dimensional wind vector eld can be dened within the

WindVectorField.m.

at the appropriate times by the

The method stored in the le is then called

Aircraft

and

Cable Model

blocks.

For the purpose of this simulation, the atmospheric movement is decoupled from the movement of the aircraft and cable through the air. This causes only the inuence of the air onto the solid bodies to be considered, while the retroactions of the solid bodies onto the wind behavior are neglected.

Cable Model, it was decided not to International Standard Atmosphere block

For reasons of numeric eort within the calculate the air density through the

21


in the Chair of Flight Dynamics library, but to perform these calculations in a small method stored in the

AirDensity.m

le.

As can be easily derived from the

thermodynamic ideal gas model of the ISA (Hen08), the air density within the troposphere is given as

ρ(h) =

p0 MAir · · R ·h T0 + ∂T ∂h

1+

∂T ∂h

·h

! −g·M∂TAir R·

∂h

(2.28)

T0

Most glider ying takes place using convective thermal or orographic ridge lift within the troposphere. Only on rare occasions using wave lift do gliders pass the tropopause and climb to stratospheric altitudes.

Since these specic operations

are irrelevant for the launch simulation, the limitations by only regarding density distribution within the troposphere are of no signicant eect. Yet, as most glider ights are thermal ights and the favorable convective instabilities form predominantly during the warm summer month of the year, winches in operation are often exposed to hot and high conditions of high density altitude. A means for degrading winch performance for temperature- and elevation-induced eects on air density has not yet been included. As already mentioned in sections 1.4, 2.1.1 and 2.1.4, no control mechanism to regulate lateral motion has been implemented in the simulation so far. This requires all sideways directed forces to be suppressed, so that the

vWind,f = 0

vWind,f -component becomes

in the ensuing analysis.

2.2 Provision of Data The simulation's comprehensive model is stored in the the main directory.

generic6DoF.mdl

This is also the location of the aircraft's aerodynamic and

inertial parameters, which are stored in the MATLAB les and

ask21_moi.mat.

Simulink model.

le in

ask21aero_edited.mat

These are loaded with the generic simulation's GUI into the

Also, several aircraft specic initial values of the simulation are

Trimmpunkte/WinchLaunch.mat. All other parameters specic to the winch simulation are stored under WinchLaunchParameters.mat, whereas this MATLAB variables le is created with the MATLAB script WinchLaunchParameters.m.

stored under

2.3 Engagement of Numeric Solution The initial conditions of the glider and cable during the rst iterative step are unaccelerated, steady movements with an strained cable. This is rooted in the fact that the incorporated 6DoF simulation initializes in unaccelerated and steady state of the aircraft. The cable is also initialized in a straight line between the glider's CG tow hook and the winch. One result of this is an initial iterative propagation of the additional strain, caused by gravity, along the cable. This takes several iteration steps to reach the glider and causes a slight oscillation of the cable force exerted onto the aircraft. The numeric solution will only stabilize after the simulation has run through several time steps. Since the beginning of the simulation - when the numeric solution has not yet engaged properly - is prone anyways to the previously 22


described physical errors, such as not regarded aircraft ground eect or cable friction on the aireld surface, this is readily accepted.

2.4 Further Limits of Models Apart from the previously mentioned characteristics and limitations, several further points need to be mentioned.

The aircraft model is that of a rigid body system,

dened as a point mass. The glider's aerodynamic and ight mechanic behavior has been parameterized in ight tests conducted at the Chair of Flight Dynamics. The resulting linear coecients have then been estimated in their nonlinear nature using the United States Air Force's and the

Digital Datcom

Stability and Control Datcom

methodology (WV76)

software.

One has to keep in mind that this is only a parameterization of the airow around the aircraft, not a precise description of it. Especially the eects during stalls and very high angles of attack are dicult to describe using these techniques.

Even

small angles of sideslip might cause an asymmetric stall during these high angles of attack and would result in a highly asymmetric ight condition. This is especially true for the ensuing analysis of the aggressive winch launch in section 3.2.9. Also, the analysis of structural eects in this thesis is only of secondary interest. For example, an overspeed of the ASK 21's maximum winch launch speed of

150km/h

is only looked at when it is excessive.

23

VW =

3 Results Safety Margin One of the primary concerns of this thesis is the safety analysis of potential critical situations, as they might occur while winch launching. It is deemed especially critical if the glider reaches a stalled state during the launch process. Because trajectory control precision is insucient during stalled ight and the glider decelerates quickly towards the stall speed when pitched upwards without an acting cable force, a cable break is one of the worst case scenarios that might occur. Due to this, the relative dierence between the aircraft's airspeed safety margin

S :=

Va

and stall speed

VS

is dened as the

S.

Va − VS Va

(3.1)

One should bear in mind that the aircraft's stall speed is proportional to the a and the aircraft's stall speed in nz = m−Z AC ·g steady ight VS,1g . The safety margin follows as: square root of the vertical load factor

Va − VS,1g · S= Va

√

nz

√ VS,1g · nz =1− Va

(3.2)

This also means that the safety margin is an expression for the angle of attack α. If ◦ the glider reaches its stalling angle of attack αS = 8 - which is also the angle of the maximum lift coecient - then the wing is completely stalled and the safety margin has reached a value of

S = 0.

3.1 Reference Simulation To properly evaluate the inuences of varying the dierent simulation parameters, the following simulation conditions have been dened as standard and will serve as the reference launch for further analysis.

All simulations are conducted using

standard atmospheric values with the aircraft initializing at sea level.

3.1.1 Reference Simulation Settings General:

Time step size

∆t = 0.01s

Wind:

No wind is present in the reference simulation:

24

(u, v, w)TWind,g = (0, 0, 0)T

Chair of Flight Dynamics RWTH Aachen University Winch:

Winch location

(x, y, z)TW,g = (1000m, 0, 0)T

Winch Operator:

PID winch force controller with time- and glider position-dependant target force

Initial target winch force

Nominal rate of change of target winch force

Maximum target winch force

FT,0 = 4000N dFT dt

= 500N/s

FT,max = 8000N

Glider:

1

(u, v, w)Tk,0 = (18.8m/s, 0, 0)T

Initial unaccelerated track speeds

Initial Euler angles

(Φ, Θ, Ψ)T0 = (0, 0, 0)T

Elevator trim angle

ηTrim = −3.0◦

CG hook location

(x, y, z)TCG-Hook,f = (0.6m, 0, 0.3m)T

Pilot:

PID airspeed controller and pitch damper engage at safety altitude

hSafety =

50m

Pilot's target airspeed

VT = 30m/s = 108km/h

IAS

Cable:

2

Synthetic cable with the following physical properties : Mechanical Property

Diameter Mass per Unit Length Modulus of Elasticity Strain-speed Stress Coecient

dc = 5.0mm m ¯ c = 1.88 · 10−2 kg/m Ec = 4.025 · 1010 P a cc = 1.56 · 107 P a · s

Derived Mechanical Property

Ac = 19.6mm2 ρc = 960kg/m3

Mean Cross Section Mean Density

Aerodynamic Properties

CD,c = 1.3

Drag Coecient note:

No data was available for the value of cc . It has been selected in such a way as to notably dampen cable vibration. Anderson (And07) provides this experimental CD,c value for the two-dimensional viscous ow over a cylinder with Re =

ρ0 ·vref ·dc µ0

=

kg ·30 m ·5.0mm s m3 kg −4 1.7894·10 m·s

1.225

≈ 1.0 · 104 .

1 In no-wind conditions, this is equivalent to the glider's stall speed in undisturbed airow

VS,1g (mAC = 510kg) = 18.8m/s (Ale80). 2 Courtesy of Rosenberger Tauwerk GmbH 25

Chair of Flight Dynamics RWTH Aachen University FEM

Model:

Initial number of elements

Initial location of elements: equally spaced along straight line between CG

n0 = 20

tow hook and winch location

3.1.2 Reference Results

Figure 3.1: Flight Path of the Reference Conguration

The simulation of the reference conguration supplies a ight path of the glider as presented in ight path diagram 3.1.

In this case, the glider will reach a release

hRelease = 439m at tRelease = 33s. For illustrative purposes, the deformed the moment of t = 15s has been plotted into the mentioned ight path

altitude of cable at

diagram. A cable deection due to acting external forces can clearly be seen against the connecting straight line between the glider and winch.

This deection seems

reasonable and shall serve as partial validation of the cable model.

Figure 3.2: Pitch and Climb Angles during Reference Launch

26


Θ and climb angle γ during t ≈ 0.3s is due to the aircraft having

Figure 3.2 illustrates the progression of the pitch angle the reference simulation. The initial dip in an insucient initial angle of attack

3

γ

at

α0 at the beginning of the simulation to support

its own weight . Especially once the glider has traversed the maximum pitch and climb angles and

γmax

at

Θmax

t ≈ 11.5s, a damped phugoid mode becomes obvious. Without the pitch Glider Pilot block, this phugoid would be more strongly

damping function of the

pronounced. Yet in practical ight operations, the damping of the phugoid mode during the winch launch is often dependent upon pilot skill.

Figure 3.3: Safety-relevant Parameters during Reference Launch A plot of safety-relevant parameters during the reference winch launch is given

S . The initial peak of t = 0.9s corresponds with the decreasing distance between airspeed Va and stall speed VS , resulting in a minimum safety margin Smin = 2.7% at

in gure 3.3 which also implicitly supplies the safety margin the angle of attack

α

at

this moment. This is partially due to the glider's descending ight path within the simulation's rst second, yet also corresponds with the necessity for rotating into a nose-up attitude for the initial climb. In practical measurements, it is expected that

Smin

would be larger than the given value, since the aircraft would not have a

negative climb angle below ground level. Instead, the glider will continue its ground roll. This serves to lessen the acting angle of attack and decrease the load factor and stall speed, making the actual launch safer in regard to the safety margin

S.

As a means of analyzing pilot behavior during the launch, the elevator deection

η

is plotted over time in gure 3.4.

The pilot will initially hold the elevator in

the steady trimmed condition until the safety altitude of at

tSafety = 4.25s.

hSafety = 50m

is reached

This marks the onset of airspeed control which can also clearly

be seen in gures 3.2 and 3.3. Airspeed acceleration

V˙ a

lessens and the controller

3 Recall that neither a ground eect model nor a ground model has been implemented in the simulation.

27


pitches the aircraft farther up to approach the target airspeed of

VT = 30m/s.

Yet,

this particular pitch-up motion appears to excite the glider's phugoid mode slightly. During the nal phase of the launch, starting at

t ≈ 21s, the pilot eventually releases

back pressure on the controls until cable release.

Figure 3.4: Elevator Deection During the Reference Launch

A plot of the winch force over time, as presented in gure 3.5, shows that the winch operator model performs its task in a satisfying manner.

During the rst

third of the simulation, the operator smoothly increases the winch force steady manner, until at

t ≈ 11s,

FC,W

in a

the maximum winch force is reached. This value

is then held nearly constant for the duration of

∆t ≈ 5s, when a subtle reduction χ increases. This allows for a

in the winch force sets in as the glider-winch-angle

smooth transition into steady and horizontal ight by the glider. By time the cable is released, the winch force will have decreased to a value of only

FC,G ≈ 2300N ,

allowing for only a small change in loads acting on the aircraft and reducing wear on materials.

Figure 3.5: Winch Force during the Reference Launch

3.2 Variation of Parameters To gain a better understanding of the physical occurrences during the winch launch process, the glider's response to changes in certain parameters is analyzed.

The

results - within the context of the underlying physical and numeric models - are then used to substantiate or rebut several working hypotheses. 28


3.2.1 Inuence of Synthetic vs. Steel Cable One of the current disputes within the soaring community is the eectiveness of replacing the previously standard steel cables with synthetic ones. A wide range of personal values of experience and empirical values, primarily regarding the gain in release altitude by using synthetic cables, can be heard. This makes a comparison of the cable types within this simulation of interest. To reach this, the cable properties have been changed to those of a steel cable: Mean Density Modulus of Elasticity Strain-speed Stress Coecient

ρc = 4250kg/m3 Ec = 1.70 · 1011 P a cc = 2.50 · 108 P a · s

note:

The cable diameter and drag coecient remain unchanged. While Dietz and Mupende (DM04) recommend an undamped steel cable model, the above value for cc has been chosen to provide adequate numeric damping.

Figure 3.6: Flight Paths with Varying Cable Types

The ight path diagram 3.6 shows a release altitude gain of

∆hRelease = 9m in favor

of the synthetic cable. This result cannot support the claim of the often mentioned signicant gains by the use of synthetic cables. Yet, their advantages in terms of weight, manageability and splicing shall remain untouched.

3.2.2 Inuence of Tow Distance In the past, winch launching has primarily taken place at general aviation airelds. There, spatial and air trac restrictions often limit the available towing distance to

dTow = 1000m or less.

4

However, temporary access of some European operators to

4 distance between the glider's take-o point and the winch location 29


larger airelds, often being inactive or little used military or commercial facilities, has brought a rise in interest on longer tow distances. At the same time, the mass increase associated with longer steel cables brought with it some inherent diculties. The constructive changes in winches necessary to accommodate the increased inertial loads caused by the signicant increase in cable mass were long considered to be elaborate. A further hindrance of increasing tow distance was the result. However, with the availability of the much lighter synthetic cables, a study of the eects of a longer tow distance seems appropriate.

Figure 3.7: Flight Paths with Variable Tow Distance

hRelease (dTow = 1000m) = 439m, hRelease (dTow = 2000m) = hRelease (dTow = 3000m) = 1097m can be taken from gure 3.7. While the increase in release altitude from the 1000m tow distance to 2000m is almost proportional, the gain decreases signicantly below a proportional value with 3000m Release altitudes of

851m

and

distance available. This overproportionate decrease might be attributed to winch operator behavior. It is not clear whether an operator would decrease the target winch force in the same manner dependant on the glider-winch-angle

χ during a longer tow

as during shorter tows. No critical conditions are expected to arise by the increase in tow distance because only the duration during which the cable force

F~G,C

acts

on the aircraft increases. Its magnitude is expected to remain unchanged. Taking these results, it can be said that at operating locations where longer tow distances are available and useable, the winch launch is a viable alternative to aerotowing. The signicantly higher tow durations with increase in tow distance cause a rise from tRelease (dTow = 1000m) = 33s to tRelease (dTow = 2000m) = 63s and tRelease (dTow = 3000m) = 85s. This, together with the notable increase cable re-

5

6 remarkably.

trieve times , will lower the maximum winching cadence

5 the time it takes to unreel and lay out the cable between the winch and the launch area 6 the number of launches that can be conducted within a given span of time 30


3.2.3 Wind Inuence Whereas the assumption of a no-wind condition in the reference simulation simplies calculation and estimation and facilitates better compatibility of the data with other works in the eld of ight mechanics, it bears only limited signicance for actual ight operations. In these, almost always some form of wind and atmospheric movement is present. Two dynamically dierent cases of wind behavior have been analyzed with the simulation; the case of a steady head- or tailwind and the case of gusts.

Head- and Tailwind Most ight regulations such as the German Glider Operation Regulations (Seg03) limit tailwind glider launch operations to very small values of wind speed or prohibit them completely. Due to this, it was expected that the release altitude of a launch conducted in tailwind conditions would decrease more strongly than that of a launch in an equally strong, yet opposing, headwind.

Figure 3.8: Flight Paths with Acting Steady Winds The simulation results, visualized in ight path diagram 3.8, cannot support this hypothesis. The glider ying in a below the reference launch and a

28m.

2.5m/s tailwind will release 2.5m/s headwind will cause

at

∆hRelease = −26m ∆hRelease =

a gain of

Though the safety plot 3.9 for the tailwind condition shows a stalled situation

in the interval of

0.6s < t < 1.2s

where the stalling angle of attack

αS

is exceeded

slightly, this has to be interpreted cautiously. A more detailed look at the ight path during this interval reveals, that the glider has descended to an altitude of

h < 0m,

due to the lack of a ground model. This cannot be interpreted as being physically meaningful, but much rather should be seen as a continuation of the ground roll. Only once sucient airspeed is reached will the glider lift o which is expected to occur at a time, when the angle of attack 31

α

is again below its stalling value.

To


provide a more meaningful safety-analysis of the situation during which the glider takes o in a slight tailwind, the inclusion of a proper ground-eect and ground model are necessary. However, the increased duration of a lower dynamic pressure acting on the aircraft becomes apparent in gure 3.9. A pilot transitioning into the climb too early - by not properly regarding the decreased airspeed at the beginning of the launch - still runs the risk of stalling the glider. A glider launch in tailwind conditions is safely possible only if the decrease in airspeed is accounted for and the pilot is not distracted by the visual impressions of a higher groundspeed.

Figure 3.9: Safety-relevant Parameters with

2.5m/s

This is not to say that tailwind operations are favorable.

Tailwind

In fact, one of the

most problematic situations for the winch operator is the control and steering of a descending cable and drag chute that is being blown towards the winch and runs the risk of passing it. Also, trac coordination between landing and departing aircraft becomes more challenging in this situation and emergency procedures such as in the event of a cable break, are also inuenced. The results should much rather be interpreted as overly rewarding launch operations with a headwind component.

Gust Response Contrary to the preceding analysis of ight paths in windy conditions, the primary concern of the gust analysis is to determine and describe the response of the cable and not the aircraft's trajectory.

The simulation is exposed to both, an instant

headwind gust and an instant updraft gust. The magnitude of each gust is and acts for the duration of

t > 9s.

In the case of the

2.5m/s

2.5m/s

headwind gust, the

glider is exposed to the wind function

T

(u, v, w)Wind,g =

(0, 0, 0)T t < 9s T (−2.5m/s, 0, 0) t ≥ 9s 32

(3.3)

Chair of Flight Dynamics RWTH Aachen University and the

2.5m/s

upwind gust is described by the wind function

T

(u, v, w)Wind,g =

(0, 0, 0)T t < 9s T (0, 0, −2.5m/s) t ≥ 9s

As a measure of cable response, the weak link force

(3.4)

7

FG,C

has been chosen.

Figure 3.10: Angle of Attack during Gusts Figure 3.10 reveals that the updraft gust causes a stronger increase in the angle of attack

α at the instant of gust onset than the headwind gust does.

Even though the

upwind gust appears to be more critical, no safety analysis is performed. An updraft gust of this magnitude is not expected to develop in close proximity to the ground because the airow is restricted to primarily horizontal movement by the ground, making a stall unlikely.

The statically stable conguration of the ASK 21 causes

the glider to respond with a pitch-down moment in the upwind gust case, but the aircraft's airspeed is increased more by the headwind gust. This is responsible for the slight pitch-up motion of the glider following the headwind gust, as can be seen in gure 3.12.

These are classic excitations of the phugoid mode in the aircraft's

longitudinal motion.

Figure 3.11: Weak Link Force Response after Gust Disturbance

Each response of the weak link force in gure 3.11, to either the vertical or horizontal gusts, can be interpreted as an overlay of a higher frequency oscillation with

7 Since the weak link sits close to the glider end of the cable, it is said that the weak link force is the absolute value of the force exerted by the cable onto the glider.

33


a small amplitude and a lower frequency oscillation with a larger amplitude. Both higher frequency oscillations have a frequency of

fhf = 2.5Hz

and appear to be well

damped. These are therefore attributed to physical and numeric oscillation of the cable due to a change in mean cable tension caused by the gusts. Their amplitudes 0 0 are of up to T1,hf ≈ 30N for the headwind gust and T1,hf ≈ 20N for the horizontal gust. These values are comparatively low and the danger of overstressing the cable due to these higher frequency vibrations is considered to be low. For future experiments, it is expected that the amplitude of the higher frequency oscillations will increase and gain more relevance for aircraft with lower wing loading as they are more susceptible to gusts.

Figure 3.12: Changes in Pitch due to Gusts

In the case of the calculations performed with the ASK 21 the lower frequency oscillations in weak link force dominate, having a frequency of

flf = 0.2Hz .

This

matches the phugoid's frequency very well, as can be seen in gure 3.12, and causes the low frequency changes in cable load to be attributed to changes in the aircraft's ight path. This oscillation's amplitude can be much larger in certain cases such as a stronger gust and might exceed the equivalent value of the weak link force in the reference condition. An accidental overload of the cable, exceeding the weak link breaking strength, seems more likely in this case.

3.2.4 Inuence of Tow Hook Location

Figure 3.13: Changes in Pitch due to Tow Hook Location

34


Another goal of this thesis is to gain a qualitative understanding of the inuence the mounting location of the CG hook has on the glider's launching behavior. Since the hook is mounted closely to the CG, and the cable force induced into the hook is of larger magnitude than the aircraft's weight, even small alterations in the moment arm are expected to signicantly modify the aircraft's longitudinal motion behavior. For the comparison of mounting positions, the hook location was moved 10cm T T forward of the reference condition's location to (x, y, z)CG-Hook,f = (0.7m, 0, 0.3m) T T and 10cm aft to (x, y, z)CG-Hook,f = (0.5m, 0, 0.3m) . The plot of gure 3.13 shows that the aft mounted hook causes slightly higher pitch angles in the rst and later phases of the launch than the reference condition or the forward mounted hook. However, the maximum pitch angle decreases from Φmax, forward = 50◦ and Φmax, ref = 48◦ to Φmax, aft = 47◦ . A more docile phugoid mode for the aft mounted hook is one of the consequences, while also providing a release altitude gain of

∆hRelease = 0.2m

to the reference condition. At the same

time, the forward mounted hook has a release altitude loss of

∆hRelease = −1.2m,

as shown in ight path plot 3.14. These changes are only menial and it is doubted that these could be eectively proven in ight tests due to the numerous other perturbations acting on the aircraft.

Figure 3.14: Inuence of CG Hook Location on Flight Path

The higher pitch angles in the initial climb phase, caused by the tow hook being in the aft position, make a safety analysis of this conguration highly recommendable. Yet gure 3.15 shows a decrease of the safety margin from reference launch to

Smin = 2.5%

Smin = 2.7%

in the

in the conguration with a farther aft CG hook.

This is only a very marginal decrease and is opposed by the reduction in pilot workload due to the more favorable longitudinal motion modes of this conguration. In light of these results it can be said that there is still potential for ight mechanically optimizing the location of the CG tow hook of the ASK 21 training glider. But at the same time, further analysis is necessary to properly evaluate the feasibility of such a design change. Particularly, the structural modications necessary 35


as well as the changes in handling quality need to be assessed. At last, the question of how other aircraft might respond to the same design changes is of interest. It is considered likely that other gliders also have further development potential in their designs to increase launch performance.

Figure 3.15: Safety-relevant Parameters with CG Hook Moved

36

10cm

Aft


3.2.5 Inuence of Winch Operator Behavior One of the main dierences in operator behavior is how fast the operator advances the winch throttle to the nal target setting. Since the winch throttle is controlled via the winch force by the Winch Operator block, the nominal rate of change in dFT winch target force , is taken as a means of modifying winch operator behavior. dt

Figure 3.16: Changes in Pitch due to Operator Behavior

dFT dt notably change the longitudinal stability of the aircraft during the launch process. The time-pitch-plot in gure 3.16 readily shows that even small changes of

A decrease in the rate of change of the target winch force will lessen the phugoid amplitude while an increase will strengthen it. The obvious consequence for the pilot is that the workload will increase when the winch throttle is opened more swiftly.

Figure 3.17: Safety-relevant Parameters for Nominal Winch Target Force Rate of dFT Change = 600N/s dt This increase in workload, along with the fact the winch force

FC,W

is higher

dFT 8 during the early parts of the tow , is expected to make an increase in more dt 8 An increase in the winch force

FC,W

results in higher pitch-up moments.

37


dFT dFT critical. Yet, gure 3.17 reveals that even a 20% increase of to = 600N/s dt dt dFT from the reference simulation value of = 500N/s causes no notable change in dt the minimum of the safety margin Smin . It remains at a value of Smin = 2.7%. The release altitude does not seem to vary much either, as shown by gure 3.18. Only a dFT , while release altitude gain of ∆hRelease = 4m is apparent by the 20% increase in dt the same absolute decrease causes only a release altitude loss of ∆hRelease = 5m. In dFT are only minor on the release general, it seems that the eects of a change in dt altitude and safety margin. But the swifter raising of the winch target force appears to require more of the pilot's attention.

Figure 3.18: Flight Paths with Varying Target Force Rate of Change

dFT dt

3.2.6 Winch Force Inuence

Figure 3.19: Elevator Deection

η

with Varying Maximum Target Forces

An obvious way to increase release altitude is to increase the winch force

FT,max

FC,W .

This

higher winch force has been achieved by varying the winch operator's nal target winch force

FT,nal .

The time during which the target force is increased from the

constant initial value of

FT,0

has also been held constant, causing a variation in the

38


dFT . Also, the upper limit of dt dened by the maximum attainable torque of the engine.

nominal rate of change in winch target force

FT,nal

is

∆hRelease = 63m between the reference simulation = 8kN ) and a maximum target force of FT,nal = 13kN is seen in ight path plot 3.20 of this numeric experiment. This value of FT,nal = 13kN is close to the maximum engine torque of TE,max = 895N m, corresponding to a winch force of FC,W,max = 13.15kN . The dierence between FT,nal = 13kN and FC,W,max = 13.15kN is said to be a necessary operational reserve for operations out of the An increase in release altitude of

(FT,nal

engine's optimal working point.

Figure 3.20: Flight Paths with Varying Maximum Target Force Operations with increased cable forces also bear some inherent risks. The weak link breaking strengths need to be increased, thereby exposing the glider to higher loads, induced at the CG hook. Currently, the ASK 21's pilot operating handbook (Ale80) allows for a maximum weak link breaking strength of

10000N ± 1000N

for winch launches, making structural strengthening mandatory for the simulated increases in target and cable forces. At the same time, gure 3.19 shows that even with a maximum target force of

FT,max = 9000n,

the pilot will hold the controls in

the full aft position for most of the tow duration. This situation is aggravated by a further increase in the maximum tow force

FT,max

and it is expected to cause an

uncompensated increase in airspeed due to the limited ight control authority. A further area of concern was that the vector of the cable induced tow force

F~G,C

is directed almost orthogonally downwards to the ight path during the later

phase 5 of the winch launch. At the same time, the magnitude of signicantly increased by raising

FT,max

and

FC,W .

F~G,C

has been

This large downwards-directed

force requires a signicant increase in lift and load factor for the aircraft to hold its altitude or continue to climb.

During this, the pilot is unaware of an increase in

load factor, since the aircraft does not accelerate in the 39

za -direction.

It has been


thought possible that the aircraft approaches a stall in this conguration and that was the reason - along with the potential increase in airspeed - for a further safety analysis of this specic launch conguration. The maximum target winch force of

FT,max = 13kN

has been determined to be the most critical case of the conducted

numeric experiments.

Figure 3.21: Safety-relevant Parameters for Maximum Target Force

Since the initial target force of

FT,0 = 4kN

FT,max = 13kN

is the same as during the reference

launch, the safety parameter has the same initial minimum of

Smin (t ≈ 1s) = 2.7%

as during the reference launch. During the second half of the winch launch, when the increased winch force has reached its maximum inuence, the safety parameter drops to a further local minimum of

Smin,loc (t ≈ 13s) = 16.3%.

While this shows that a

sucient margin to the stall is being held in this launch conguration, it is obvious by the variations in airspeed that the limited elevator authority makes airspeed control dicult for the pilot. (Ale80) of

Even though the ASK 21's maximum winch launch speed

VW = 150km/h = 41.7m/s

is briey exceeded by

1.7m/s = 6.1km/h,

it is expected that this is not structurally critical and that there is development potential in the ASK 21's airframe for a structural solution. It is also supposed that a strengthening of aircraft's primary structure is possible to support the increase in loads acting on the tow hook. Under these structural assumptions, the presented results support the thesis that a notable increase in tow force can raise release altitudes by a signicant margin.

3.2.7 Inuence of Cable Model In an attempt to gain a more detailed understanding of the physical mechanisms governing the inuence of the tow cable on the release altitude of the glider, the standard model presented in section 2.1.3 was modied.

40

Particularly, the ight


paths of the following cable models have been determined and are presented in the ight path diagram 3.22:

FEM with Tension, Gravity and Drag

is the model described in section 2.1.3 and

regards all presented inertial, internal and external forces.

FEM with Tension and Drag, no Gravity

selectively disregards the inuence of

gravity as it would act on the cable while retaining the eects of internal and inertial forces and aerodynamic drag.

FEM with Tension and Gravity, no Drag

selectively disregards the inuence of

aerodynamic drag on the cable.

FEM with Tension, no Gravity and Drag

completely disregards the external forces

acting on deforming the cable. Cable deformation is only due to internal and inertial forces.

Secant Model

is the physical limit case of a massless ideal cable without aerody-

namic drag.

It is reached by orienting the winch force along a connecting

straight line between the winch an the glider's CG hook.

Figure 3.22: Inuence of Dierent Physical Cable Models on Flight Path

The ight path plot of gure 3.22 shows two distinct sets of ight paths, the changing inuence between the sets being the aerodynamic drag.

At the same

time, the ight paths regarding gravity lay below the corresponding ight paths without gravitational inuence on the cable.

This said, it can be estimated that

the gravitational inuence causes a release altitude loss of the drag inuence is

∆hRelease ≈ −32m.

∆hRelease ≈ −2m whereas

It is peculiar to note that the ight paths

of the ideal secant model and the FEM with tension, no gravity and drag model are identical for all practical purposes. 41

These negligible dierences in the


trajectory serve to show that the inertial forces acting on the cable in the launch are also negligible. Several development impulses can be drawn from the presented inuence of cable models. On the numeric side, the development of a modied secant model with drag and gravitational inuence might be favorable.

The above mentioned tendencies

show that a good correlation between this new model and the reference model might be achieved, while signicantly reducing the numeric complexity and increasing the stability of the current algorithms.

At times, the occurring numeric instabilities

have restricted the use of the cable mode of section 2.1.3.

Also, the assumption

of section 2.1.3, which states that the rendered cable power is negligible, should be challenged. The eect that the aerodynamic cable drag has on the attainable release altitude seems too large to neglect this part of the energy balance. It is evident that drag seems to more directly inuence the cable than gravity does. This is also supported by the change in release altitude that was presented in section 3.2.1.

The introduction of synthetic cables into winch launching has

primarily modied the cable material density while the cable cross section remains circular to oval with similar diameters to the steel cable. For the future, it is thought to be likely that more prominent gains in release altitude will be reached by reducing the cable diameter and causing lower aerodynamic cable drag. This, however, can only be realized with the availability of cable bers able to withstand the higher tension in the cable caused by a reduced cross section.

3.2.8 Inuence of Cable Drag Coecient

Figure 3.23: Flight Paths with Varying Cable Drag Coecient

CD,C

The previous section 3.2.7 identies the aerodynamic drag acting on the cable as one of the primary inuences on release altitude

CD,C

hRelease .

Since the cable drag coecient

has so far been estimated and the cable drag model assumes that the cable 42


is a smooth cylinder, the questions of the susceptibility of the launch behavior to changes in drag arises. Figure 3.23 shows that a drag reduction of launch to

CD,C = 0.6,

54%,

from

CD,C = 1.3 in the reference hRelease = 17m. This

results in an release altitude gain of

is almost twice as much as has been gained by the change from a steel cable to a synthetic one. If cable bers are available that support a signicant reduction of the cable diameter safely, then it is expected that the lower drag will cause a notable increase in release altitudes in actual ight operations.

3.2.9 Analysis of Aggressive Pilot Behavior While so far, no highly critical situations in winch launching have been discussed,

9

the benet and risks associated with an aggressive winch launch , as performed by some pilots, has also been looked at. During such an aggressive winch launch, the pilot will pitch the glider to a steep pitch angle while still in close proximity to the ground, intending to maximize the altitude gain. Before the launch, he or she will usually have placed the elevator trim in an aft position.

Figure 3.24: Flight Path of Aggressively Flown Winch Launch

hSafety = −10m, Fading Unit to experience the unit step already during the simulation's

To allow for this maneuvering, the safety altitude has been set to causing the

rst iteration.

This setup allows for the higher rotating speeds in the pitch axis

necessary to reach the higher pitch and climb angles early.

At the same time,

the pilot already begins to track and control airspeed close to the ground. Both of these behaviors are thought to be adequate representations of actual aggressive pilot ◦ behavior. Also, the elevator trim angle has been set to ηTrim = −7.0 , corresponding to approximately

1/3rd

aft stick position.

9 This is the German colloquial Kavalierstart. 43


The altitude gain brought by this behavior is plotted in gure 3.24 and has a value of

∆hRelease = 22m.

Especially the higher climb gradient close to ground

level is prominent in the plot where the ight paths of the reference launch and the aggressive launch quickly diverge. A comparison of the airspeed and stall speed clearly discloses the risk associated with this pilot behavior. Figure 3.25 shows that during the time frame of

0.7s < t

Numeric Simulation of a Glider Winch Launch - RWTH-Aachen

Numeric Simulation of a Glider Winch Launch - RWTH-Aachen

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